they really don't see the irony

Marginalizing the free expression of speech and/or classifying another's exercise of free speech as hate speech is bigoted and hate speech in and of itself.

I would hate to think myself so weak and mentally fragile that I tremble and cower in the face of disagreeable words and had to have someone save me from so much as seeing such unpleasant letter groupings.

Alas, that is the state of things.

Social media outlets are not suppressing first amendment rights. Social media outlets are suppressing hate speech or are they? Hate speech is not free speech

Hate speech to you may not be hate speech to me. A free society does not allow the government to decide that. The federal government has paid and pressured social media to suppress ideas it doesn't like under the penumbra of hate speech. This is a violation of the first amendment.

"Hate speech to you may not be hate speech to me."

Because conservatives believe "hate speech is free speech" yet it is completely different.

"A free society does not allow the government to decide that. The federal government has paid and pressured social media to suppress ideas it doesn't like under the penumbra of hate speech. This is a violation of the first amendment."

At the moment, not all hate speech is protected by the First Amendment, since hateful expression can fall within certain, narrow categories of unprotected speech such as:

Incitement to imminent lawless action (incitement);
speech that threatens serious bodily harm (true threats); or
speech that causes an immediate breach of the peace (fighting words).

https://www.thefire.org/news/hate-speech-protected-first-amendment

The first amendment came out at the same time as the second amendment which came out in the bill of rights.

https://www.archives.gov/founding-docs/bill-of-rights/what-does-it-say

Also, The First Amendment has not been amended, which means that Americans have the same laws on free speech since late 1791 (which means all hate speech needs to be excluded from the first amendment).

https://www.nas.org/academic-questions/30/3/amending_the_first_amendment
https://www.archives.gov/founding-docs/bill-of-rights-transcript

How about not using the term hate speech as a cudgel to deny others their use of free speech. Hate speech works in the same sense climate change works- it's undefinable, thus can be used whenever necessary.

How has hate speech got to do with climate change other than the fact that climate change is real and so is hate speech?

Hate speech seeks to compel behavior, just as climate change does. Freedom and compelled behavior don't coexist well

Not a good reference but using your reference. I could say that conservative's hate speech seeks to compel their behaviour to be violent, yet climate change seeks to compel Climate Denial just for Conservatives to create a political football.

But your other point "freedom and compelled behaviour don't coexist well" you're right